Prelude:atanh from fay-base-0.20.0.1

Average Error: 0.0 → 0.0

Time: 1.6s

Precision: binary64

Cost: 448

Math

\[\frac{x + 1}{1 - x} \]

↓

\[\frac{x + 1}{1 - x} \]

FPCore

(FPCore (x) :precision binary64 (/ (+ x 1.0) (- 1.0 x)))

↓

(FPCore (x) :precision binary64 (/ (+ x 1.0) (- 1.0 x)))

C

double code(double x) {
	return (x + 1.0) / (1.0 - x);
}

↓

double code(double x) {
	return (x + 1.0) / (1.0 - x);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x + 1.0d0) / (1.0d0 - x)
end function

↓

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x + 1.0d0) / (1.0d0 - x)
end function

Java

public static double code(double x) {
	return (x + 1.0) / (1.0 - x);
}

↓

public static double code(double x) {
	return (x + 1.0) / (1.0 - x);
}

Python

def code(x):
	return (x + 1.0) / (1.0 - x)

↓

def code(x):
	return (x + 1.0) / (1.0 - x)

Julia

function code(x)
	return Float64(Float64(x + 1.0) / Float64(1.0 - x))
end

↓

function code(x)
	return Float64(Float64(x + 1.0) / Float64(1.0 - x))
end

MATLAB

function tmp = code(x)
	tmp = (x + 1.0) / (1.0 - x);
end

↓

function tmp = code(x)
	tmp = (x + 1.0) / (1.0 - x);
end

Wolfram

code[x_] := N[(N[(x + 1.0), $MachinePrecision] / N[(1.0 - x), $MachinePrecision]), $MachinePrecision]

↓

code[x_] := N[(N[(x + 1.0), $MachinePrecision] / N[(1.0 - x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

   \[\frac{x + 1}{1 - x} \]

2. Final simplification 0.0

   \[\leadsto \frac{x + 1}{1 - x} \]

Alternatives

Alternative 1
Error	1.2
Cost	584

\[\begin{array}{l} t_0 := -1 + \frac{-2}{x}\\ \mathbf{if}\;x \leq -558.1019768123572:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.7588418466906802 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	0.9
Cost	584

\[\begin{array}{l} t_0 := -1 + \frac{-2}{x}\\ \mathbf{if}\;x \leq -558.1019768123572:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.7588418466906802 \cdot 10^{-6}:\\ \;\;\;\;1 + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	1.5
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -558.1019768123572:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.7588418466906802 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4
Error	32.5
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2022300 
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1.0) (- 1.0 x)))